修正的SQP型并行变量分配算法  

A Modified SQP Parallel Variable Distribution Algorithm

作　　者：冯婷婷[1] 韩丛英[2,1] 贺国平[1] 

机构地区：[1]山东科技大学信息科学与工程学院,山东青岛266510 [2]中国科学院研究生院数学科学学院,北京100049

出　　处：《数学物理学报（A辑）》2012年第2期336-343,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11101420,10971122);高等学校博士点基金(20093718110005);山东省科技攻关(2009GG10001012);山东省自然科学基金(Y2008A01)资助

摘　　要：Ferris和Mangasarian提出求解最优化问题的PVD(并行变量分配)算法,此算法是把变量分为主要变量和辅助变量,分配到p个处理机上,每个处理机除了负责更新本处理机的主要变量外,同时还沿着给定的方向更新辅助变量,使算法的鲁棒性和灵活性得到了很大的提高.该文基于文献[6]提出一种修正的SQP型PVD算法,构造其搜索方向是下降方向和可行方向的组合,并对此方向给予一个高阶修正,使此算法很好地防止Maratos效应发生,而且能够克服在求解子问题时出现约束不相容的情况.在合适的条件下,推导出此算法具有全局收敛性.Ferris and Mangasarian proposed a PVD（parallel variable distribution） algorithm for solving optimization problems, which divides variables into primary and secondary variables groups. According to the algorithm, the variables are distributed among p parallel processors with each processor having the responsibility for updating its primary variables while allowing the remaining ＂secondary＂ variables to change in a restricted fashion along some easily com- putable directions, which enhances robustness and flexibility of the algorithm. In this paper, we present a modified SQP type PVD algorithm based on [6], whose search direction is a suitable combination of a descent direction and a feasible direction, and give a second-order revised for such a direction. This new algorithm is very effective in preventing Maratos effect from hap- pening, and avoid constraints in subproblem are inconsistent. We show the global convergence under some suitable conditions.

关 键 词：非线性规划 序列二次规划 PVD算法. 

分 类 号：O211.2[理学—概率论与数理统计]